Scaling limits for PDE-based simulation
Paul Fischer, Katherine L. Heisey, Misun Min · 2015
Parallel computing is founded on the principle that, given enough work for a given problem, one can subdivide the computation across P processors and realize an effective P -fold reduction in time to solution. On today’s architectures, any PDE-based or particle-based simulation that uses a billion gridpoints or particles can easily be distributed across two compute nodes and run in half the time—for essentially the same power—compared with running on just a single node. This computational scenario, running a problem of fixed size in half the time on two processors or nearly one-P th the time on P processors, is termed strong scaling and is the focus of this paper. Specifically, we explore the basic question of how far one can scale a given problem, defined by its computational resolution n (e.g., the number of gridpoints), when using P processors. The relevance of the strong scaling question is expressed succinctly in the equation